# ISEE Upper Level Math : How to divide exponents

## Example Questions

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### Example Question #24 : Exponential Operations

Simplify:

Explanation:

Separate the fraction and apply the quotient of powers rule:

### Example Question #31 : Exponential Operations

Simplify:

Explanation:

Apply the quotient of powers rule.

### Example Question #32 : Exponential Operations

Evaluate:

The expression is undefined

Explanation:

Any nonzero number raised to the power of 0 is equal to 1, so , and

### Example Question #33 : Exponential Operations

Evaluate:

The expression is undefined.

The expression is undefined.

Explanation:

Any nonzero number raised to the power of 0 is equal to 1, so . Therefore,

However, an expression with a denominator of 0 is undefined, so that is the correct choice.

### Example Question #34 : Exponential Operations

Simplify:

Explanation:

Based on the negative exponent rule we have:

Which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents.So we have:

Separate the equation:

### Example Question #35 : Exponential Operations

Simplify:

Explanation:

Based on the zero-exponent rule we have:

That means any non-zero number raised to the zero power is equal to . So we can write:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. In addition based on the negative exponent rule we have:

Which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

### Example Question #36 : Exponential Operations

Evaluate:

Explanation:

First we need to subtract the numbers in parentheses. So we can write:

We can alternatively write:

### Example Question #1 : How To Divide Exponents

Simplify:

Explanation:

Based on the quotient rule for exponents, we know that for any non-zero number  and any integers  and ,

.

We should separate the fraction and apply the quotient rule for exponents:

### Example Question #91 : Numbers And Operations

Simplify:

Explanation:

Based on the quotient rule for exponents, we know that for any non-zero number  and any integers  and ,

.

We also know that any non-zero number raised to the power of is .

### Example Question #92 : Numbers And Operations

Simplify:

Explanation:

We know that any non-zero number raised to the power of is equal to

Now factor:

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